My daughter started in a twin bed just before her 2nd birthday. Mainly because that's all we had, and she fell out of her crib and onto her head(SCARY!) the night before. That was it for me. She didn't really have any problems with the transition. Ours has the drawers on the bottom part of the bed too, and I was wary of the height. We have it against the wall, with bed rails on both sides, and she's never fallen out.
However, you are the best judge as to whether she's ready or not. I have friends whose children have moved at 4, and some who've moved at 18 months. It all depends on the readiness of your babygirl. Ask her what she thinks too, so she knows she's part of the decision process. It could make the transition easier, for both of you since you would know she was ok with it herself, and she may see it as really becoming a "big girl".